BC 


MM    E5D 


LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 

GIFT  OF 


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THE  UNIVERSITY  OF  CHICAGO 

FOUNDED  BY  JOHN  D.  ROCKEFELLER 


THE  NATURE  OF  HYPOTHESIS 


A  DISSERTATION 

SUBMITTED  TO  THE  FACULTY  OF  THE  GRADUATE  SCHOOL  OF  ARTS  AND 

LITERATURE  IN  CANDIDACY  FOR  THE  DEGREE  OF 

DOCTOR  OF  PHILOSOPHY 

(DEPARTMENT  OF  PHILOSOPHY) 


BY 

MYRON  LUCIUS  ASHLEY 


CHICAGO 
1903 


[The  chapter  constituting  this  Dissertation  is  taken  from  a  larger  volume 
entitled  Studies  in  Logical  Theory,  which  has  appeared  as  Volume  XI,  Second 
Series,  of  the  Decennial  Publications  of  the  University  of  Chicago.] 


[For  the  pages  on  Mill  and  Whewell 
the  author  wishes  to  acknowledge  his 
indebtedness  to  Professor  Dewey.j 


FEINTED  AT  THE  UNIVERSITY  OF  CHICAGO  PEESS 


or  THE 
(   UNIVERSITY   ) 


YII 

THE  NATURE  OF  HYPOTHESIS 

IN  the  various  discussions  of  the  hypothesis  which  have 
appeared  in  works  on  inductive  logic  and  in  writings  on 
scientific  method,  its  structure  and  function  have  received 
considerable  attention,  while  its  origin  has  been  compara- 
tively neglected.  *  The  hypothesis  has  generally  been  treated 
as  that  part  of  scientific  procedure  which  marks  the  stage 
where  a  definite  plan  or  method  is  proposed  for  dealing  with 
new  or  unexplained  facts.  It  is  regarded  as  an  invention 
for  the  purpose  of  explaining  the  given,  as  a  definite  con- 
jecture which  is  to  be  tested  by  an  appeal  to  experience  to 
see  whether  deductions  made  in  accordance  with  it  will  be 
found  true  in  fact.  The  function  of  the  hypothesis  is  to 
unify,  to  furnish  a  method  of  dealing  with  things,  and  its 
structure  must  be  suitable  to  this  end.  It  must  be  so 
formed  that  it  will  be  likely  to  prove  valid,  and  writers 
have  formulated  various  rules  to  be  followed  in  the  forma- 
tion of  hypotheses.  These  rules  state  the  main  require- 
ments of  a  good  hypothesis,  and  are  intended  to  aid  in  a 
general  way  by  pointing  out  certain  limits  within  which  it 
must  fall. 

In  respect  to  the  origin  of  the  hypothesis,  writers  have 
usually  contented  themselves  with  pointing  out  the  kind  of 
situations  in  which  hypotheses  are  likely  to  appear.  But 
after  this  has  been  done,  after  favorable  external  conditions 
have  been  given,  the  rest  must  be  left  to  "genius,"  for 
hypotheses  arise  as  "happy  guesses,"  for  which  no  rule  or 
law  can  be  given.  In  fact,  the  genius  differs  from  the 
ordinary  plodding  mortal  in  just  this  ability  to  form  fruitful 

143 


144  STUDIES  IN  LOGICAL  THEORY 

hypotheses  in  the  midst  of  the  same  facts  which  to  other  less 
gifted  individuals  remain  only  so  many  disconnected  expe- 
riences. 

This  unequal  stress  which  has  been  laid  on  the  structure 
and  function  of  the  hypothesis  in  comparison  with  its  origin 
may  be  attributed  to  three  reasons:  (1)  The  facts,  or  data, 
which  constitute  the  working  material  of  hypotheses  are 
regarded  as  given  to  all  alike,  and  all  alike,  are  more  or  less 
interested  in  systematizing  and  unifying  experience.  The 
purpose  of  the  hypothesis  and  the  opportunity  for  forming  it 
are  thus  practically  the  same  for  all,  and  hence  certain  defi- 
nite rules  can  be  laid  down  which  will  apply  to  all  cases 
where  hypotheses  are  to  be  employed.  (2)  But  beyond  this 
there  seems  to  be  no  clue  that  can  be  formulated.  There  is 
apparently  a  more  or  less  open  acceptance  of  the  final  answer 
of  the  boy  Zerah  Colburn,  who,  when  pressed  to  give  an 
explanation  of  his  method  of  instantaneous  calculation,  ex- 
claimed in  despair:  "God  put  it  into  my  head,  and  I  can't 
put  it  into  yours." l  (3)  And,  furthermore,  there  is  very  often 
a  strong  tendency  to  disregard  investigation  into  the  origin 
of  that  which  is  taken  as  given,  for,  since  it  is  already 
present,  its  origin,  whatever  it  may  have  been,  can  have 
nothing  to  do  with  what  it  is  now.  The  facts,  the  data, 
are  here,  and  must  be  dealt  with  as  they  are.  Their  past, 
their  history  or  development,  is  entirely  irrelevant.  So, 
even  if  we  could  trace  the  hypothesis  farther  back  on  the 
psychological  side,  the  investigation  would  be  useless,  for 
the  rules  to  which  a  good  hypothesis  must  conform  would 
remain  the  same. 

Whether  or  not  it  can  be  shown  that  Zerah  Colburn's 
ultimate  explanation  is  needed  in  logic  as  little  as  Laplace 
asserted  a  similar  one  to  be  required  in  his  celestial  me- 

i  DE  MORGAN,  Budget  of  Paradoxes,  pp.  55,  56 ;  quoted  by  WELTON,  Logic,  Vol. 
II,  p.  60. 


THE  NATUBE  OF  HYPOTHESIS  145 

chanics,  it  may  at  least  be  possible  to  defer  it  to  some,  extent 
by  means  of  a  further  psychological  inquiry.  It  will  be 
found  that  psychological  inquiry  into  the  origin  of  the 
hypothesis  is  not  irrelevant  in  respect  to  an  understanding 
of  its  structure  and  function ;  for  origin  and  function  can- 
not be  understood  apart  from  each  other,  and,  since  struc- 
ture must  be  adapted  to  function,  it  cannot  be  independent 
of  origin.  In  fact,  origin,  structure,  and  function  are  organ- 
ically connected,  and  each  loses  its  meaning  when  absolutely 
separated  from  each  other.  It  will  be  found,  moreover,  that 
the  data  which  are  commonly  taken  as  the  given  material 
are  not  something  to  which  the  hypothesis  is  subsequently 
applied,  but  that,  instead  of  this  external  relation  between 
data  and  hypothesis,  the  hypothesis  exercises  a  directive  func- 
tion in  determining  what  are  the  data.  In  a  word,  the  main 
object  of  this  discussion  will  be  to  contend  against  making 
a  merely  convenient  and  special  way  of  regarding  the 
hypothesis  a  full  and  adequate  one.  Though  we  speak  of 
facts  and  of  hypotheses  that  may  be  applied  to  them,  it 
must  not  be  forgotten  that  there  are  no  facts  which  remain 
the  same  whatever  hypothesis  be  applied  to  them ;  and  that 
there  are  no  hypotheses  which  are  hypotheses  at  all  except 
in  reference  to  their  function  in  dealing  with  our  subject- 
matter  in  such  a  way  as  to  facilitate  its  factual  apprehension. 
Data  are  selected  in  order  to  be  determined,  and  hypotheses 
are  the  ways  in  which  this  determination  is  carried  on.  If, 
as  we  shall  attempt  to  show,  the  relation  between  data  and 
hypothesis  is  not  external,  but  strictly  correlative,  it  is  evi- 
dent that  this  fact  must  be  taken  into  account  in  questions 
concerning  deduction  and  induction,  analytic  and  synthetic 
judgments,  and  the  criterion  of  truth.  Its  bearing  must  be 
recognized  in  the  investigation  of  metaphysical  problems  as 
well,  for  reality  cannot  be  independent  of  the  knowing 
process.  In  a  word,  the  purpose  of  this  discussion  of  the 


146  STUDIES  IN  LOGICAL  THEOEY 

hypothesis  is  to  determine  its  nature  a  little  more  precisely 
through  an  investigation  of  its  rather  obscure  origin,  and  to 
call  attention  to  certain  features  of  its  function  which  have 
not  generally  been  accorded  their  due  significance. 


The  hypothesis  as  predicate. — It  is  generally  admitted 
that  the  function  of  the  hypothesis  is  to  provide  a  way  of 
dealing  with  the  data  or  subject-matter  which  we  need  to 
organize.  In  this  use  of  the  hypothesis  it  appears  in  the 
rCle  of  predicate  in  a  judgment  of  which  the  data,  or  facts, 
to  be  construed  constitute  the  subject. 

In  his  attempts  to  reduce  the  movements  of  the  planets 
about  the  sun  to  some  general  formula,  Kepler  finally  hit 
upon  the  law  since  known  as  Kepler's  law,  viz.,  that  the 
squares  of  the  periodic  times  of  the  several  planets  are  pro- 
portional to  the  cubes  of  their  mean  distances  from  the  sun. 
This  law  was  first  tentatively  advanced  as  a  hypothesis. 
Kepler  was  not  certain  of  its  truth  till  it  had  proved  its 
claim  to  acceptance.  Neither  did  Newton  have  at  first  any 
great  degree  of  assurance  in  regard  to  his  law  of  gravitation, 
and  was  ready  to  give  it  up  when  he  failed  in  his  first  attempt 
to  test  it  by  observation  of  the  moon.  And  the  same  thing 
may  be  said  about  the  caution  of  Darwin  and  other  investi- 
gators in  regard  to  accepting  hypotheses.  The  only  reason 
for  their  extreme  care  in  not  accepting  at  once  their  tentative 
formulations  or  suggestions  was  the  fear  that  some  other 
explanation  might  be  the  correct  one.  •  This  rejection  of 
other  possibilities  is  the  negative  side  of  the  matter.  We 
become  confident  that  our  hypothesis  is  the  right  one  as  we 
lose  confidence  in  other  possible  explanations ;  and  it  might 
be  added,  without  falling  into  a  circle,  that  we  lose  confidence 
in  the  other  possibilities  as  we  become  more  convinced  of 
our  hypothesis. 


THE  NATURE  OF  HYPOTHESIS  147 

It  appears  that  such  may  be  the  relation  of  the  positive 
and  negative  sides  in  case  of  such  elaborate  hypotheses  as 
those  of  Kepler  and  Newton;  but  is  it  true  where  our 
hypotheses  are  more  simple?  It  is  not  easy  to  understand 
why  the  fact  that  the  hypothesis  is  more  simple,  and  the 
time  required  for  its  formulation  and  test  a  good  deal 
shorter,  should  materially  change  the  state  of  affairs.  The 
question  remains:  Why,  if  there  is  no  opposition,  should 
there  be  any  uncertainty  ?  In  all  instances,  then,  the  hypothe- 
sis appears  as  one  among  other  possible  predicates  which 
may  be  applied  to  our  data  taken  as  subject-matter  of  a 
judgment. 

The  predicate  as  hypothesis.  —  Suppose,  then,  the 
hypothesis  is  a  predicate;  is  the  predicate  necessarily  a 
hypothesis?  This  is  the  next  question  we  are  called  upon 
to  answer,  and,  since  the  predicate  cannot  very  well  be  taken 
aside  from  the  judgment,  our  question  involves  the  nature 
of  the  judgment. 

While  it  will  not  be  necessary  to  give  a  very  complete 
account  of  the  various  definitions  of  the  judgment  that  might 
be  adduced,  still  the  mention  of  a  few  of  the  more  prominent 
ones  may  serve  to  indicate  that  something  further  is  needed. 
In  definitions  of  the  judgment  sometimes  the  subjective  side 
is  emphasized,  sometimes  the  objective  side,  and  in  other 
instances  there  are  attempts  to  combine  the  two.  For 
instance,  Lotze  regards  the  judgment  as  the  idea  of  a  unity 
or  relation  between  two  concepts,  with  the  further  implica- 
tion that  this  connection  holds  true  of  the  object  referred 
to.  J.  S.  Mill  says  that  every  proposition  either  affirms  or 
denies  existence,  coexistence,  sequence,  causation,  or  resem- 
blance. Trendelenburg  regards  the  judgment  as  a  form  of 
thought  which  corresponds  to  the  real  connection  of  things, 
while  Ueberweg  states  the  case  a  little  differently,  and  says 
that  the  essence  of  judgment  consists  in  recognizing  the 


148  STUDIES  IN  LOGICAL  THEORY 

objective  validity  of  a  subjective  connection  of  ideas.  Royce 
points  to  a  process  of  imitation  and  holds  that  in  the  judg- 
ment we  try  to  portray  by  means  of  the  ideas  that  enter  into 
it.  Ideas  are  imitative  in  their  nature.  Sigwart's  view  of 
the  judgment  is  that  in  it  we  say  something  about  some- 
thing. With  him  the  judgment  is  a  synthetic  process,  while 
Wundt  considers  its  nature  analytic  and  holds  that,  instead 
of  uniting,  or  combining,  concepts  into  a  whole,  it  separates 
them  out  of  a  total  idea  or  presentation.  Instead  of  blend- 
ing parts  into  a  whole,  it  seuarates  the  whole  into  its  con- 
stituent parts.  Bradley  and  Bosanquet  both  hold  that  in 
the  judgment  an  ideal  content  comes  into  relation  with 
reality.  Bradley  says  that  in  every  judgment  reality  is 
qualified  by  an  idea,  which  is  symbolic.  The  ideal  content 
is  recognized  as  such,  and  is  referred  to  a  reality  beyond  the 
act.  This  is  the  essence  of  judgment.  Bosanquet  seems 
to  perceive  a  closer  relation  between  idea  and  reality,  for 
although  he  says  that  judgment  is  the  "intellectual  function 
which  defines  reality  by  significant  ideas,"  he  also  tells  us 
that  "the  subject  is  both  in  and  out  of  the  judgment,  as 
Reality  is  both  in  and  out  of  my  consciousness." 

In  all  these  definitions  of  judgment  the  predicate  appears 
as  ideal.  An  ideal  content  is  predicated  of  something, 
whether  we  regard  this  something  as  an  idea  or  as  reality 
beyond,  or  as  reality  partly  within  and  partly  without  the 
act  of  judging ;  and  it  is  ideal  whether  we  consider  it  as  one 
of  the  three  parts  into  which  judgments  are  usually  divided, 
or  whether  we  say,  with  Bosanquet  and  Bradley,  that  sub- 
ject, predicate,  and  copula  all  taken  together  form  a  single 
ideal  content,  which  is  somehow  applied  to  reality.  More- 
over, we  not  only  judge  about  reality,  but  it  seems  to  be 
quite  immaterial  to  reality  whether  we  judge  concerning  it 
or  not. 
9  Many  of  our  judgments  prove  false.  Not  only  do  we  err 


THE  NATURE  OF  HYPOTHESIS  149 

in  our  judgments,  but  we  often  hesitate  in  making  them  for 
fear  of  being  wrong;  we  feel  there  are  other  possibilities, 
and  our  predication  becomes  tentative.  Here  we  have  some- 
thing very  like  the  hypothesis,  for  our  ideal  content  shows 
itself  to  be  a  tentative  attempt  in  the  presence  of  alterna- 
tives to  qualify  and  systematize  reality.  It  appears,  then, 
on  the  basis  of  the  views  of  the  judgment  that  have  been 
mentioned,  that  not  only  do  we  find  the  hypothesis  taking 
its  place  as  the  predicate  of  a  judgment,  but  the  predicate  is 
itself  essentially  of  the  nature  of  a  hypothesis. 

In  the  views  of  the  judgment  so  far  brought  out,  reality, 
with  which  it  is  generally  admitted  that  the  judgment 
attempts  to  deal  in  some  way,  appears  to  lie  outside  the  act 
of  judging.  Now,  everyone  would  say  that  we  make  some 
advance  in  judging,  and  that  we  have  a  better  grasp  of 
things  after  than  before.  But  how  is  this  possible  if  reality 
lies  without  or  beyond  our  act  of  judging  ?  Is  the  reality 
we  now  have  the  same  that  we  had  to  begin  with  ?  If  so, 
then  we  have  made  no  advance  as  far  as  the  real  itself  is 
concerned.  If  merely  our  conception  of  it  has  changed, 
then  it  is  not  clear  why  we  may  not  be  even  worse  off  than 
before.  If  reality  does  lie  beyond  our  judgment,  then  how, 
in  the  nature  of  the  case,  can  we  ever  know  whether  we 
have  approached  it  or  have  gone  still  farther  away?  To 
make  any  claim  of  approximation  implies  that  we  do  reach 
reality  in  some  measure,  at  least,  and,  if  so,  it  is  difficult  to 
understand  how  it  lies  beyond,  and  is  independent  of,  the 
act  of  judging. 

Further  analysis  of  judgment. —  It  remains  to  be  seen 
whether  a  further  investigation  of  the  judgment  will  still 
show  the  predicate  to  be  a  hypothesis.  It  is  evident  that  in 
some  cases  the  judgment  appears  at  the  end  of  a  more  or 
less  pronounced  reflective  process,  during  which  other  pos- 
sible judgments  have  suggested  themselves,  but  have  been 


150  STUDIES  IN  LOGICAL  THEORY 

rejected.  The  history  of  scientific  discovery  is  filled  with 
cases  which  illustrate  the  nature  of  the  process  by  which  a 
new  theory  is  developed.  For  instance,  in  Darwin's  Forma- 
tion of  Vegetable  Mould  through  the  Action  of  Earth  Worms, 
we  find  the  record  of  successive  steps  in  the  development  of 
his  hypothesis.  Darwin  suspected  from  his  observations  that 
vegetable  mold  was  due  to  some  agency  which  was  not  yet 
determined.  He  reasoned  that  if  vegetable  mold  is  the  result 
of  the  life-habits  of  earthworms,  i.  e.,  if  earth  is  brought  up 
by  them  from  beneath  the  surface  and  afterward  spread  out 
by  wind  and  rain,  then  small  objects  lying  on  the  surface  of  the 
ground  would  tend  to  disappear  gradually  below  the  surface. 
Facts  seemed  to  support  his  theory,  for  layers  of  red  sand, 
pieces  of  chalk,  and  stones  were  found  to  have  disappeared 
below  the  surface  in  a  greater  or  less  degree.  A  common 
explanation  had  been  that  heavy  objects  tend  to  sink  in  soft 
soil  through  their  own  weight,  but  the  earthworm  hypothe- 
sis led  to  a  more  careful  examination  of  the  data.  It  was 
found  that  the  weight  of  the  object  and  the  softness  of  the 
ground  made  no  marked  difference,  for  sand  and  light  objects 
sank,  and  the  ground  was  not  always  soft.  In  general,  it 
was  shown  that  where  earthworms  were  found  vegetable 
mold  was  also  present,  and  vice  versa. 

In  this  investigation  of  Darwin's  the  conflicting  explana- 
tions of  sinking  stones  appear  within  the  main  question  of 
the  formation  of  vegetable  mold  by  earthworms.  The  facts 
that  disagreed  with  the  old  theory  about  sinking  stones  were 
approached  through  this  new  one.  But  the  theories  had  some- 
thing in  common,  viz.,  the  disappearance  of  the  stones  or 
other  objects :  they  differed  in  their  further  determination  of 
this  disappearance.  In  this  case  it  may  seem  as  if  the  facts 
which  were  opposed  to  the  current  theory  of  sinking  stones 
were  seen  to  be  discrepant  only  after  the  earthworm  hypothe- 
sis had  been  advanced;  the  conflict  between  the  new  facts 


THE  NATURE  OF  HYPOTHESIS  151 

and  the  old  theory  appears  to  have  arisen  through  the  influ- 
ence of  the  new  theory. 

•  There  are  cases,  however,  where  the  facts  seem  clearly  to 
contradict  the  old  theory  and  thus  give  rise  to  a  new  one. 
For  example,  we  find  in  Darwin's  introduction  to  his  Origin 
of  Species  the  following:  "In  considering  the  origin  of 
species  it  is  quite  conceivable  that  a  naturalist  reflecting  on 
the  mental  affinities  of  organic  beings,  on  their  embryologi- 
cal  relations,  their  geographical  distribution,  geological  suc- 
cession, and  other  such  facts,  might  come  to  the  conclusion 
that  species  had  not  been  independently  created  but  had 
descended,  like  varieties,  from  other  species."  It  would 
seem  from  this  statement  that  certain  data  were  found  for 
which  the  older  theory  of  independent  creation  did  not  offer 
an  adequate  explanation.  And  yet  the  naturalist  would 
hardly  "reflect"  on  all  these  topics  in  a  comparative  way 
unless  some  other  mode  of  interpretation  were  already  dawn- 
ing upon  him,  which  led  him  to  review  the  accepted  reflec- 
tions or  views. 

As  a  more  simple  illustration,  we  may  cite  the  common 
experience  of  a  person  who  is  uncertain  concerning  the 
identity  of  an  approaching  object,  say,  another  person.  At 
first  he  may  not  be  sure  it  is  a  person  at  all.  He  then  sees 
that  it  is  someone,  and  as  the  person  approaches  he  is  inclined 
to  believe  him  to  be  an  acquaintance.  As  the  supposed 
acquaintance  continues  to  approach,  the  observer  may  dis- 
tinguish certain  features  that  cause  him  to  doubt,  and  then 
relinquish  his  supposition  that  it  is  an  acquaintance.  Or, 
he  may  conclude  at  once  that  the  approaching  person  is 
another  individual  he  knows,  and  the  transition  may  be  so 
readily  made  from  one  to  the  other  that  it  would  be  difficult 
to  determine  whether  the  discordant  features  are  discordant 
before  the  new  supposition  arises,  or  whether  they  are  not 
recognized  as  conflicting  till  this  second  person  is  in  mind. 


152  STUDIES  IN  LOGICAL  THEORY 

Or,  again,  the  identification  of  the  new  individual  and  the 
discovery  of  the  features  that  are  in  conflict  with  the  first 
supposition  may  appear  to  go  on  together.  • 

Now,  marked  lines  of  likeness  appear  between  this 
relatively  simple  judgment  and  the  far  more  involved  ones 
of  scientific  research.  •  In  the  more  extended  scientific 
process  we  find  data  contradicting  an  old  theory  and  a  new 
hypothesis  arising  to  account  for  them.  The  hypothesis  is 
tested,  and  along  with  its  verification  we  have  the  rejection, 
or  rather  the  modification,  of  the  old  theory.  Similarly,  in 
case  of  the  approaching  stranger  all  these  features  are 
present,  though  in  less  pronounced  degree.  In  scientific 
investigation  there  is  an  interval  of  testing  by  means  of  more 
careful  consideration  of  the  data  and  even  actual  experimen- 
tation. Before  an  explanation  is  accepted  subject  to  test,  a 
number  of  others  may  have  been  suggested  and  rejected. 
They  may  not  have  received  even  explicit  recognition.  In 
case  of  the  identification  of  the  stranger  this  feature  is 
also  present.  Between  two  fairly  definite  attempts  to 
identify  the  mind  does  not  remain  a  mere  blank  or  station- 
ary, but  other  possible  identifications  may  be  suggested 
which  do  not  have  sufficient  plausibility  to  command  serious 
attention;  they  are  only  comparatively  brief  suggestions  or 
tendencies. 

It  is  to  be  noted  that  in  all  these  instances  the  first  sup- 
position was  not  entirely  abandoned,  but  was  modified  and 
more  exactly  determined.  (Why  it  could  not  be  wholly 
false  and  the  new  one  wholly  new,  will  be  considered  later 
in  connection  with  discussion  of  the  persistence  and  re- 
formation of  habit.)  There  was  such  a  modification  of  the 
old  theory  as  would  meet  the  requirements  of  the  new  data, 
and  the  new  explanations  thus  contained  both  old  and  new 
features. 

We  have  seen  that  the  predicate  of  the   scientific   judg- 


51  I  T 

CM 

^ 

THE  NATURE  OF  HYPOTHESIS  153 

ment  is  a  hypothesis  which  is  consciously  applied  to  certain 
data.  If  the  similarity  between  the  scientific  judgment  and 
the  more  immediate  and  simple  judgment  is  to  be  main- 
tained, it  is  clear  that  the  predicate  of  the  simple  judgment 
must  be  of  like  nature.  The  structure  of  the  two  varieties 
of  judgment  differs  only  in  the  degree  of  explicitness  which 
the  hypothesis  acquires.  That  is,  the  predicate  of  a  judg- 
ment, as  such,  is  ideal;  it  is  meaning,  significant  quality. 
If  conditions  are  such  as  to  make  the  one  judging  hesitant 
or  doubtful  the  mind  wavers;  the  predicate  is  not  applied 
at  once  to  the  determination  or  qualification  of  data,  and 
hence  comes  to  more  distinct  consciousness  on  its  own 
account.  From  being  "  ideal,"  it  becomes  an  idea.  Yet  its 
sole  purpose  and  value  remains  in  its  possible  use  to  inter- 
pret data.  Let  the  idea  remain  detached,  and  let  the  query 
whether  it  be  a  true  predicate  (i.  e.,  really  fit  to  be  employed 
in  determining  the  present  data)  become  more  critical,  and 
the  idea  becomes  clearly  a  hypothesis.1  In  other  words,  the 
hypothesis  is  just  the  predicate-function  of  judgment  defi- 
nitely apprehended  and  regarded  with  reference  to  its  nature 
and  adequacy. 

Psychological  analysis  of  judgment. — This  hypothetical 
nature  of  the  predicate  will  be  even  more  apparent  after  a 
further  psychological  analysis,  which,  while  applying  more 
directly  to  the  simpler  and  more  immediate  judgments,  may 
be  extended  to  the  more  involved  ones  as  well. 

In  psychological  terms,  we  may  say,  in  explanation  of 
the  judging  process,  that  some  stimulus  to  action  has  failed 
to  function  properly  as  a  stimulus,  and  that  the  activity 

^Advanced  grammarians  treat  this  matter  in  a  way  which  should  be  instructive 
to  logicians.  The  hypothesis,  says  SWEET  (§  295  of  A  New  English  Grammar,  Logical 
and  Historical,  Oxford,  1892),  suggests  an  affirmation  or  negation  "as  objects  of 
thought.1'  "  In  fact,  we  often  say  supposing  (that  is,  '  thinking ')  it  is  true,  instead 
of  if  it  is  true.''1  In  a  word,  the  hypothetical  judgment  as  such  puts  explicitly  before 
us  the  content  of  thought,  of  the  predicate  or  hypothesis ;  and  in  so  far  is  a  moment 
in  judgment  rather  than  adequate  judgment  itself. 


154  STUDIES  IN  LOGICAL  THEORY 

which  was  going  on  has  thus  been  interrupted.  Response 
in  the  accustomed  way  has  failed.  In  such  a  case  there 
arises  a  division  in  experience  into  sensation  content  as  sub- 
ject and  ideal  content  as  predicate.  In  other  words,  an 
activity  has  been  going  on  in  accordance  with  established 
habits,  but  upon  failure  of  the  accustomed  stimulus  to  be 
longer  an  adequate  stimulus  this  particular  activity  ceases, 
and  is  resumed  in  an  integral  form  only  when  a  new  habit 
is  set  up  to  which  the  new  or  altered  stimulus  is  adequate.  It 
is  in  this  process  of  reconstruction  that  subject  and  predicate 
appear.  Sensory  quality  marks  the  point  of  stress,  or" 
seeming  arrest,  while  the  ideal  or  imaged  aspect  defines  the 
continuing  activity  as  projected,  and  hence  that  with  which 
start  is  to  be  made  in  coping  with  the  obstacle.  It  serves  as 
standpoint  of  regard  and  mode  of  indicated  behavior.  The 
sensation  stands  for  the  interrupted  habit,  while  the  image 
stands  for  the  new  habit,  that  is,  the  new  way  of  dealing 
with  the  subject-matter.1 

It  appears,  then,  that  the  purpose  of  the  judgment  is  to 
obtain  an  adequate  stimulus  in  that,  when  stimulus  and 
response  are  adjusted  to  each  other,  activity  will  be  resumed. 
But  if  this  reconstruction  and  response  were  to  follow  at 
once,  would  there  be  any  clearly  defined  act  of  judging  at 
all?  In  such  a  case  there  would  be  no  judgment,  properly 
speaking,  and  no  occasion  for  it.  There  would  be  simply  a 
ready  transition  from  one  line  of  activity  to  another;  we 
should  have  changed  our  method  of  reaction  easily  and 
readily  to  meet  the  new  requirements.  On  the  one  hand, 
our  subject-matter  would  not  have  become  a  clearly  recog- 
nized datum  with  which  we  must  deal ;  on  the  other  hand, 
there  would  be  no  ideal  method  of  construing  it.2  Activity 

1  This  carries  with  it,  of  course,  the  notion  that  "  sensation  "  and  "  image  "  are 
not  distinct  psychical  existences  in  themselves,  but  are  distinguished  logical  forces. 

2  Concerning  the  strict  correlativity  of  subject  and  predicate,  data  and  hypo- 
thesis, see  pp.  182,m 


THE  NATURE  OF  HYPOTHESIS  155 

would  have  changed  without  interruption,  and  neither  sub- 
ject nor  predicate  would  have  arisen. 

In  order  that  judgment  may  take  place  there  must  be 
interruption  and  suspense.  Under  what  conditions,  then,  is 
this  suspense  and  uncertainty  possible  ?  Our  reply  must  be 
that  we  hesitate  because  of  more  or  less  sharply  denned 
alternatives ;  we  are  not  sure  which  predicate,  which  method 
of  reaction,  is  the  right  one.  The  clearness  with  which 
these  alternatives  come  to  mind  depends  upon  the  degree  of 
explicitness  of  the  judgment,  or,  more  exactly,  the  explicit- 
ness  of  the  judgment  depends  upon  the  sharpness  of  these 
alternatives.  Alternatives  may  be  carefully  weighed  one 
against  the  other,  as  in  deliberative  judgments ;  or  they  may 
be  scarcely  recognized  as  alternatives,  as  in  the  case  in  the 
greater  portion  of  our  more  simple  judgments  of  daily  con- 
duct. 

The  predicate  is  essentially  hypothetical. — If  we  review 
in  a  brief  resume"  the  types  of  judgment  we  have  considered, 
we  find  in  the  explicit  scientific  judgment  a  fairly  well- 
defined  subject-matter  which  we  seek  further  to  determine. 
Different  suggestions  present  themselves  with  varying 
degrees  of  plausibility.  Some  are  passed  by  as  soon  as 
they  arise.  Others  gain,  a  temporary  recognition.  Some 
are  explicitly  tested  with  resulting  acceptance  or  rejec- 
tion. The  acceptance  of  any  one  explanation  involves  the 
rejection  of  some  other  explanation.  During  the  process  of 
verification  or  test  the  newly  advanced  supposition  is  recog- 
nized to  be  more  or  less  doubtful.  Besides  the  hypothesis 
which  is  tentatively  applied  there  is  recognized  the  possi- 
bility of  others.  In  the  disjunctive  judgment  these  possible 
reactions  are  thought  to  be  limited  to  certain  clearly  defined 
alternatives,  while  in  the  less  explicit  judgments  they  are 
not  so  clearly  brought  out.  Throughout  the  various  forms 
of  judgment,  from  the  most  complex  and  deliberate  down  to 


156  STUDIES  IN  LOGICAL  THEORY 

the  most  simple  and  immediate,  we  found  that  a  process 
could  be  traced  which  was  like  in  kind  and  varied  only  in 
degree.  And,  finally,  in  the  most  immediate  judgments 
where  some  of  these  features  seem  to  disappear,  the  same 
account  not  only  appears  to  be  the  most  reasonable  one,  but 
there  is  the  additional  consideration,  from  the  psychological 
side,  that  were  not  the  judgment  of  this  doubtful,  tentative 
character,  it  would  be  difficult  to  understand  how  there  could 
be  judgment  as  distinct  from  a  reflex.  It  appears,  then,  that 
throughout,  the  predicate  is  essentially  of  the  nature  of  a 
hypothesis  for  dealing  with  the  subject-matter.  And,  how- 
ever simple  and  immediate,  or  however  involved  and  pro- 
longed, the  judgment  may  be,  it  is  to  be  regarded  as 
essentially  a  process  of  reconstruction  which  aims  at  the 
resumption  of  an  interrupted  experience ;  and  when  experi- 
ence has  become  itself  a  consciously  intellectual  affair,  at  the 
restoration  of  a  unified  objective  situation. 

II 

Criticism  of  certain  views  concerning  the  hypothesis. — 
The  explanation  we  have  given  of  the  hypothesis  will  enable 
us  to  criticise  the  treatment  it  has  received  from  the 
empirical  and  the  rationalistic  schools.  We  shall  endeavor 
to  point  out  that  these  schools  have,  in  spite  of  their  opposed 
views,  an  assumption  in  common  —  something  given  in  a 
fixed,  or  non-instrumental  way ;  and  that  consequently  the 
hypothesis  is  either  impossible  or  else  futile. 

Bacon  is  commonly  recognized  as  a  leader  in  the  reac- 
tionary inductive  movement,  which  arose  with  the  decline 
of  scholasticism,  and  will  serve  as  a  good  example  of  the 
extreme  empirical  position.  In  place  of  authority  and  the 
deductive  method,  Bacon  advocated  a  return  to  nature  and 
induction  from  data  given  through  observation.  The  new 
method  which  he  advanced  has  both  a  positive  and  a 


THE  NATUBE  OF  HYPOTHESIS  157 

negative  side.  Before  any  positive  steps  can  be  taken,  the 
mind  must  be  cleared  of  the  various  false  opinions  and 
prejudices  that  have  been  acquired.  This  preliminary  task 
of  freeing  the  mind  from  "phantoms,"  or  "eidola,"  which 
Bacon  likened  to  the  cleansing  of  the  threshing-floor,  having 
been  accomplished,  nature  should  be  carefully  interrogated. 
There  must  be  no  hasty  generalization,  for  the  true  method 
"collects  axioms  from  sense  and  particulars,  ascending  con- 
tinuously and  by  degrees,  so  that  in  the  end  it  arrives  at 
the  most  general  axioms."  These  axioms  of  Bacon's  are 
generalizations  based  on  observation,  and  are  to  be  applied 
deductively,  but  the  distinguishing  feature  of  Bacon's 
induction  is  its  carefully  graduated  steps.  Others,  too,  had 
proceeded  with  caution  (for  instance  Galileo),  but  Bacon  laid 
more  stress  than  they  on  the  subordination  of  steps. 

It  is  evident  that  Bacon  left  very  little  room  for  hypothe- 
ses, and  this  is  in  keeping  with  his  aversion  to  anticipa- 
tion of  nature  by  means  of  "phantoms"  of  any  sort;  he 
even  said  explicitly  that  "  our  method  of  discovery  in  science 
is  of  such  a  nature  that  there  is  not  much  left  to  acuteness 
and  strength  of  genius,  but  all  degrees  of  genius  and  intel- 
lect are  brought  nearly  to  the  same  level."1  Bacon  gave  no 
explanation  of  the  function  of  the  hypothesis ;  in  his  opinion 
it  had  no  lawful  place  in  scientific  procedure  and  must  be 
banished  as  a  disturbing  element.  Instead  of  the  recipro- 
cal relation  between  hypothesis  and  data,  in  which  hypothe- 
sis is  not  only  tested  in  experience,  but  at  the  same  time 
controls  in  a  measure  the  very  experience  which  tests  it, 
Bacon  would  have  a  gradual  extraction  of  general  laws  from 
nature  through  direct  observation.  iHe  is  so  afraid  of  the 
distorting  influence  of  conception  that  he  will  have  nothing 
to  do  with  conception  upon  any  terms,  j  So  fearful  is  he  of 
the  influence  of  pre- judgment,  of  prejudice,  that  he  will  have 

1  Novum  Organum,  Vol.  I,  p.  61. 


158  STUDIES  IN  LOGICAL  THEORY 

no  judging  which  depends  upon  ideas,  since  the  idea 
involves  anticipation  of  the  fact.  Particulars  are  some- 
how to  arrange  and  classify  themselves,  and  to  record  or 
register,  in  a  mind  free  from  conception,  certain  generaliza- 
tions. Ideas  are  to  be  registered  derivatives  of  the  given 
particulars.  This  view  is  the  essence  of  empiricism  as  a 
logical  theory.  If  the  views  regarding  the  logic  of  thought 
before  set  forth  are  correct,  it  goes  without  saying  that  such 
empiricism  is  condemned  to  self-contradiction.  It  endeavors 
to  construct  judgment  in  terms  of  its  subject  alone;  and 
the  subject,  as  we  have  seen,  is  always  a  co-respondent  to  a 
predicate — an  idea  or  mental  attitude  or  tendency  of  intellec- 
tual determination.  Thus  the  subject  of  judgment  can  be  deter- 
mined only  with  reference  to  a  corresponding  determination 
of  the  predicate.  Subject  and  predicate,  fact  and  idea,  are  con- 
temporaneous, not  serial  in  their  relations  (see  pp.  110—12). 

Less  technically  the  failure  of  Bacon's  denial  of  the  worth 
of  hypothesis — which  is  in  such  exact  accord  with  empiri- 
cism in  logic — shows  itself  in  his  attitude  toward  experi- 
mentation and  toward  observation.  Bacon's  neglect  of 
experimentation  is  not  an  accidental  oversight,  but  is  bound 
up  with  his  view  regarding  the  worthlessness  of  conception 
or  anticipation.  To  experiment  means  to  set  out  from  an 
idea  as  well  as  from  facts,  and  to  try  to  construe,  or  even  to 
discover,  facts  in  accordance  with  the  idea.  Experimenta- 
tion not  only  anticipates,  but  strives  to  make  good  an  antici- 
pation. Of  course,  this  struggle  is  checked  at  every  point 
by  success  or  failure,  and  thus  the  hypothesis  is  continuously 
undergoing  in  varying  ratios  both  confirmation  and  transfor- 
mation. But  this  is  not  to  make  the  hypothesis  secondary  to 
the  fact.  It  is  simply  to  remain  true  to  the  proposition  that 
the  distinction  and  the  relationship  of  the  two  is  a  thoroughly 
contemporaneous  one.  But  it  is  impossible  to  draw  any 
fixed  line  between  experimentation  and  scientific  observa- 


THE  NATURE  OF  HYPOTHESIS  159 

tions.  To  insist  upon  the  need  of  systematic  observation 
and  collection  of  particulars  is  to  set  up  a  principle  which  is 
as  distinct  from  the  casual  accumulation  of  impressions  as 
it  is  from  nebulous  speculation.  If  there  is  to  be  observa- 
tion of  a  directed  sort,  it  must  be  with  reference  to  some 
problem,  some  doubt,  and  this,  as  we  have  seen,  is  a  stimu- 
lus which  throws  the  mind  into  a  certain  attitude  of  response. 
Controlled  observation  is  inquiry,  it  is  search ;  consequently 
it  must  be  search  for  something.  Nature  cannot  answer 
interrogations  excepting  as  such  interrogations  are  put;  and 
the  putting  of  a  question  involves  anticipation.  The  observer 
does  not  inquire  about  anything  or  look  for  anything  except- 
ing as  he  is  after  something.  This  search  implies  at  once 
the  incompleteness  of  the  particular  given  facts,  and  the 
possibility — that  is  ideal — of  their  completion. 

It  was  not  long  until  the  development  of  natural  science 
compelled  a  better  understanding  of  its  actual  procedure 
than  Bacon  possessed.  Empiricism  changed  to  experimen- 
talism.  With  experimentalism  inevitably  came  the  recog- 
nition of  hypotheses  in  observing,  collecting,  and  comparing 
facts.  It  is  clear,  for  instance,that  Newton's  fruitful  investi- 
gations are  not  conducted  in  accordance  with  the  Baconian 
notion.  It  is  quite  clear  that  his  celebrated  four  rules  for 
philosophizing1  are  in  truth  statements  of  certain  principles 
which  are  to  be  observed  /fn  forming  hypotheses.  They 
imply  that  scientific  technique  had  advanced  to  a  point 

1  Newton's  "  Rules  for  Philosophizing  "  (Principia,  Book  III)  are  as  follows: 

Rule  I.  "No  more  causes  of  natural  things  are  to  be  admitted  than  such  as  are 
both  true,  and  sufficient  to  explain  the  phenomena  of  those  things." 

Rule  II.  "  Natural  effects  of  the  same  kind  are  to  be  referred  as  far  as  possible 
to  the  same  causes.  ' 

Rule  III.  "  Those  qualities  of  bodies  that  can  neither  be  increased  nor  dimin- 
ished in  intensity,  and  which  are  found  to  belong  to  all  bodies  within  reach  of  our 
experiments  are  to  be  regarded  as  qualities  of  all  bodies  whatever." 

Rule  IV.  "In  experimental  philosophy  propositions  collected  by  induction 
from  phenomena  are  to  be  regarded  either  as  accurately  true  or  very  nearly  true 
notwithstanding  any  contrary  hypothesis,  till  other  phenomena  occur,  by  which  they 
are  made  more  accurate,  or  are  rendered  subject  to  exceptions." 


160  STUDIES  IN  LOGICAL  THEORY 

where  hypotheses  were  such  regular  and  indispensable  fac- 
tors that  certain  uniform  conditions  might  be  laid  down  for 
their  use.  The  fourth  rule  in  particular  is  a  statement  of 
the  relative  validity  of  hypothesis  as  such  until  there  is 
ground  for  entertaining  a  contrary  hypothesis. 

The  subsequent  history  of  logical  theory  in  England  is 
conditioned  upon  its  attempt  to  combine  into  one  system  the 
theories  of  empiristic  logic  with  recognition  of  the  procedure 
of  experimental  science.  This  attempt  finds  its  culmination 
in  the  logic  of  John  Stuart  Mill.  Of  his  interest  in  and 
fidelity  to  the  actual  procedure  of  experimental  science,  as 
he  saw  it,  there  can  be  no  doubt.  Of  Jiis  good  faith  in  con- 
cluding his  Introduction  with  the  words  following  there  can 
be  no  doubt:  "I  can  conscientiously  affirm  that  no  one 
proposition  laid  down  in  this  work  has  been  adopted  for  the 
sake  of  establishing,  or  with  any  reference  for  its  fitness  in 
being  employed  in  establishing,  preconceived  opinions  in 
any  department  of  knowledge  or  of  inquiry  on  which  the 
speculative  world  is  still  undecided."  Yet  Mill  was  equally 
attached  to  the  belief  that  ultimate  reality,  as  it  is  for  the 
human  mind,  is  given  in  sensations,  independent  of  ideas ; 
and  that  all  valid  ideas  are  combinations  and  convenient 
ways  of  using  such  given  material.  Mill's  very  sincerity  made 
it  impossible  that  this  belief  should  not  determine,  at  every 
point,  his  treatment  of  the  thinking  process  and  of  its  various 
instrumentalities. 

In  Book  III,  chap.  14,  Mill  discusses  the  logic  of  expla- 
nation, and  in  discussing  this  topic  naturally  finds  it  neces- 
sary to  consider  the  matter  of  the  proper  use  of  scientific 
hypotheses.  This  is  conducted  from  the  standpoint  of  their 
use  as  that  is  reflected  in  the  technique  of  scientific  dis- 
covery. In  Book  IV,  chap.  2,  he  discusses  "Abstraction  or 
the  Formation  of  Conceptions  "  —  a  topic  which  obviously 
involves  the  forming  of  hypotheses.  In  this  chapter,  his  con- 


THE  NATURE  or  HYPOTHESIS  161 

sideration  is  conducted  in  terms,  not  of  scientific  procedure, 
but  of  general  philosophical  theory,  and  this  point  of  view 
is  emphasized  by  the  fact  that  he  is  opposing  a  certain  view 
of  Dr.  Whewell. 

The  contradiction  between  the  statements  in  the  two 
chapters  will  serve  to  bring  out  the  two  points  already  made, 
viz.,  the  correspondent  character  of  datum  and  hypothesis, 
and  the  origin  of  the  latter  in  a  problematic  situation  and  its 
consequent  use  as  an  instrument  of  unification  and  solution. 
Mill  first  points  out  that  hypotheses  are  invented  to  enable 
the  deductive  method  to  be  applied  earlier  to  phenomena; 
that  it  does  this  by  suppressing  the  first  of  the  three  steps, 
induction,  ratiocination,  and  verification.  He  states  that : 

The  process  of  tracing  regularity  in  any  complicated,  and  at 
first  sight  confused,  set  of  appearances  is  necessarily  tentative;  we 
begin  by  making  any  supposition,  even  a  false  one,  to  see  what  con- 
sequences will  follow  from  it;  and  by  observing  how  these  differ 
from  the  real  phenomena,  we  learn  what  corrections  to  make  in  our 

assumption Neither  induction  nor  deduction  would  enable 

its  to  understand  even  the  simplest  phenomena,  if  we  did  not 
often  commence  by  anticipating  the  results;  by  making  a  provi- 
sional supposition,  at  first  essentially  conjectural,  as  to  some  of  the 
very  notions  which  constitute  the  final  object  of  the  inquiry.1 

If  in  addition  we  recognize  that,  according  to  Mill,  our 
direct  experience  of  nature  always  presents  us  with  a  compli- 
cated and  confused  set  of  appearances,  we  shall  be  in  no 
doubt  as  to  the  importance  of  ideas  as  anticipations  of  a  pos- 
sible experience  not  yet  had.  Thus  he  says: 

The  order  of  nature,  as  perceived  at  a  first  glance,  presents  at 
every  instant  a  chaos  followed  by  another  chaos.  We  must  decom- 
pose each  chaos  into  single  facts.  We  must  learn  to  see  in  the 
chaotic  antecedent  a  multitude  of  distinct  antecedents,  in  the  cha- 
otic consequent  a  multitude  of  distinct  consequents.2 

iBook  HI,  chap.  2,  sec.  5;  italics  mine.  The  latter  part  of  the  passage,  begin- 
ning with  the  words  "  If  we  did  not  often  commence,"  etc.,  is  quoted  by  Mill  from 
Comte.  The  words  "  neither  induction  nor  deduction  would  enable  us  to  understand 
even  the  simplest  phenomena"  are  his  own. 

2  Book  III,  chap.  7,  sec.  1. 


162  STUDIES  IN  LOGICAL  THEORY 

In  the  next  section  of  the  same  chapter  he  goes  on  to  state 
that,  having  discriminated  the  various  antecedents  and  con- 
sequents, we  then  "  are  to  inquire  which  is  connected  with 
which."  This  requires  a  still  further  resolution  of  the  complex 
and  of  the  confused.  To  effect  this  we  must  vary  the  cir- 
cumstances; we  must  modify  the  experience  as  given  with 
reference  to  accomplishing  our  purpose.  To  accomplish 
this  purpose  we  have  recourse  either  to  observation  or  to 
experiment:  "We  may  either  find  an  instance  in  nature 
suited  to  our  purposes,  or,  by  an  artificial  arrangement  of 
circumstances,  make  one"  (the  italics  in  "suited  to  our  pur- 
pose" are  mine;  the  others  are  Mill's).  He  then  goes  on  to 
say  that  there  is  no  real  logical  distinction  between  observa- 
tion and  experimentation.  The  four  methods  of  experimen- 
tal inquiry  are  expressly  discussed  by  Mill  in  terms  of  their 
worth  in  singling  out  and  connecting  the  antecedents  and 
consequents  which  actually  belong  together,  from  the  chaos 
and  confusion  of  direct  experience. 

We  have  only  to  take  these  statements  in  their  logical 
connection  with  each  other  (and  this  connection  runs  through 
the  entire  treatment  by  Mill  of  scientific  inquiry),  to  recog- 
nize the  absolute  necessity  of  hypothesis  to  undertaking  any 
directed  inquiry  or  scientific  operation.  Consequently  we 
are  not  surprised  at  finding  him  saying  that  ' '  the  function 
of  hypotheses  is  one  which  must  be  reckoned  absolutely 
indispensable  in  science ;"  and  again  that  "  the  hypothesis 
by  suggesting  observations  and  experiments  puts  us  on  the 
road  to  independent  evidence."1 

Since  Mill's  virtual  retraction,  from  the  theoretical  point 
of  view,  of  what  is  here  said  from  the  standpoint  of  scientific 
procedure,  regarding  the  necessity  of  ideas  is  an  accompani- 
ment of  his  criticism  of  Whewell,  it  will  put  the  discussion 
in  better  perspective  if  we  turn  first  to  Whewell's  views.2 

1  Book  III,  chap.  14,  sees.  4  and  5. 

2  WILLIAM  WHEWELL,  The  Philosophy  of  the  Inductive  Sciences,  London,  1840. 


THE  NATURE  OF  HYPOTHESIS  163 

The  latter  began  by  stating  a  distinction  which  easily  might 
have  been  developed  into  a  theory  of  the  relation  of  fact  and 
idea  which  is  in  line  with  that  advanced  in  this  chapter,  and 
indeed  in  this  volume  as  a  whole.  He  questions  (chap.  2) 
the  fixity  of  the  distinction  between  theory  and  practice. 
He  points  out  that  what  we  term  facts  are  in  effect  simply 
accepted  inferences;  and  that  what  we  call  theories  are 
describable  as  facts,  in  proportion  as  they  become  thoroughly 
established.  A  true  theory  is  a  fact.  "All  the  great  theories 
which  have  successively  been  established  in  the  world  are 
now  thought  of  as  facts."  "The  most  recondite  theories 
when  firmly  established  are  accepted  as  facts ;  the  simplest 
facts  seem  to  involve  something  of  the  nature  of  theory." 

The  conclusion  is  that  the  distinction  is  a  historic  one, 
depending  upon  the  state  of  knowledge  at  the  time,  and 
upon  the  attitude  of  the  individual.  What  is  theory  for  one 
epoch,  or  for  one  inquirer  in  a  given  epoch,  is  fact  for  some 
other  epoch,  or  even  for  some  other  more  advanced  inquirer 
in  the  same  epoch.  It  is  theory  when  the  element  of  infer- 
ence involved  in  judging  any  fact  is  consciously  brought 
out;  it  is  fact  when  the  conditions  are  such  that  we  have 
never  been  led  to  question  the  inference  involved,  or  else, 
having  questioned  it,  have  so  thoroughly  examined  into  the 
inferential  process  that  there  is  no  need  of  holding  it  further 
before  the  mind,  and  it  relapses  into  unconsciousness  again. 
"If  this  greater  or  less  consciousness  of  our  own  internal  act 
be  all  that  distinguishes  fact  from  theory,  we  must  allow  that 
the  distinction  is  still  untenable  "  (untenable,  that  is  to  say, 
as  a  fixed  separation).  Again,  "fact  and  theory  have  no 
essential  difference  except  in  the  degree  of  their  certainty 
and  familiarity.  Theory,  when  it  becomes  firmly  estab- 
lished and  steadily  lodged  in  the  mind  becomes  fact."  (P.  45; 
italics  mine.)  And,  of  course,  it  is  equally  true  that  as  fast 
as  facts  are  suspected  or  doubted,  certain  aspects  of  them 


164  STUDIES  IN  LOGICAL  THEORY 

are  transferred  into  the  class  of  theories  and  even  of  mere 
opinions. 

I  say  this  conception  might  have  been  developed  in  a 
way  entirely  congruous  with  the  position  of  this  chapter. 
This  would  have  happened  if  the  final  distinction  between 
fact  and  idea  had  been  formulated  upon  the  basis  simply  of 
the  points,  "  relative  certainty  and  familiarity."  From 
this  point  of  view  the  distinction  between  fact  and  idea  is 
one  purely  relative  to  the  doubt-inquiry  function.  It  has 
to  do  with  the  evolution  of  an  experience  as  regards  its  con- 
scious surety.  It  has  its  origin  in  problematic  situations. 
Whatever  appears  to  us  as  a  problem  appears  as  contrasted 
with  a  possible  solution.  Whatever  objects  of  thought  refer 
particularly  to  the  problematic  side  are  theories,  ideas, 
hypotheses;  whatever  relates  to  the  solution  side  is  surety, 
unquestioned  familiarity,  fact.  This  point  of  view  makes 
the  distinctions  entirely  relative  to  the  exigencies  of  the  pro- 
cess of  reflective  transformation  of  experience. 

Whewell,  however,  had  no  sooner  started  in  this  train  of 
thought  than  he  turns  his  back  upon  it.  In  chap.  3  he  trans- 
forms what  he  had  proclaimed  to  be  a  relative,  historic,  and 
working  distinction  into  a  fixed  and  absolute  one.  He 
distinguishes  between  sensations  and  ideas,  not  upon  a 
genetic  basis  with  reference  to  establishing  the  conditions 
of  further  operation ;  but  with  reference  to  a  fundamentally 
fixed  line  of  demarkation  between  what  is  passively  given  to 
the  mind  and  the  activity  put  forth  by  the  mind.  Thus  he 
reinstates  in  its  most  generalized  and  fixed,  and  therefore 
most  vicious,  form  the  separation  which  he  has  just  rejected. 
Sensations  are  a  brute  unchangeable  element  of  fact  which 
exists  and  persists  independent  of  ideas;  an  idea  is  a 
mode  of  mental  operation  which  occurs  and  recurs  in  an 
independent  individuality  of  its  own.  If  he  had  carried  out 
the  line  of  thought  with  which  he  began,  sensation  as  fact 


THE  NATURE  OF  HYPOTHESIS  165 

would  have  been  that  residuum  of  familiarity  and  certainty 
which  cannot  be  eliminated,  however  much  else  of  an  expe- 
rience is  dissolved  in  the  inner  conflict.  Idea  as  hypothe- 
sis or  theory  would  have  been  the  corresponding  element 
in  experience  which  is  necessary  to  redintegrate  this  resi- 
duum into  a  coherent  and  significant  experience. 

But  since  "Whewell  did  not  follow  out  his  own  line  of 
thought,  choosing  rather  to  fall  back  on  the  Kantian  anti- 
thesis of  sense  and  thought,  he  had  no  sooner  separated  his 
fact  and  idea,  his  given  datum  and  his  mental  relation,  than 
he  is  compelled  to  get  them  together  again.  The  idea  be- 
comes "a  general  relation  which  is  imposed  upon  perception 
by  an  act  of  the  mind,  and  which  is  different  from  anything 
which  our  senses  directly  offer  to  us"  (p.  26).  Such  con- 
ceptions are  necessary  to  connect  the  facts  which  we  learn 
from  our  senses  into  truths.  "  The  ideal  conception  which 
the  mind  itself  supplies  is  superinduced  upon  the  facts  as 
they  are  originally  presented  to  observation.  Before  the 
inductive  truth  is  detected,  the  facts  are  there,  but  they  are 
many  and  unconnected.  The  conception  which  the  dis- 
coverer applies  to  them  gives  them  connection  and  unity." 
(P.  42.)  All  induction,  according  to  Whewell,  thus  depends 
upon  superinduction — imposition  upon  sensory  data  of  cer- 
tain ideas  or  general  relations  existing  independently  in 
the  mind.1 

We  do  not  need  to  present  again  the  objections  already 
offered  to  this  view:  the  impossibility  of  any  orderly  stimu- 
lation of  ideas  by  facts,  and  the  impossibility  of  any  check 
in  the  imposition  of  idea  upon  fact.  "Facts"  and  concep- 
tion are  so  thoroughly  separate  and  independent  that  any 
sensory  datum  is  indifferently  and  equally  related  to  any 
conceivable  idea.  There  is  no  basis  for  "  superinducing" 

i  The  essential  similarity  between  Whewell's  view  and  that  of  Lotze,  already  dis- 
cussed (see  chap.  3)  is  of  course  explainable  on  the  basis  of  their  common  relation- 
ship to  Kant. 


166  STUDIES  IN  LOGICAL  THEORY 

one  idea  or  hypothesis,  rather  than  any  other,  upon  any 
particular  set  of  data. 

In  the  chapter  already  referred  to  upon  abstraction,  or 
the  formation  of  conceptions,  Mill  seizes  upon  this  difficulty. 
Yet  he  and  Whewell  have  one  point  in  common:  they  both 
agree  in  the  existence  of  a  certain  subject-matter  which  is 
given  for  logical  purposes  quite  outside  of  the  logical  pro- 
cess itself.  Mill  agrees  with  Whewell  in  postulating  a 
raw  material  of  pure  sensational  data.  In  criticising  Whew- 
ell's  theory  of  superinduction  of  idea  upon  fact,  he  is 
therefore  led  to  the  opposite  assertion  of  the  complete  depend- 
ence of  ideas  as  such  upon  the  given  facts  as  such  —  in 
other  words,  he  is  led  to  a  reiteration  of  the  fundamental 
Baconian  empiricism;  and  thus  to  a  virtual  retraction  of 
what  he  had  asserted  regarding  the  necessity  of  ideas  to 
fruitful  scientific  inquiry,  whether  in  the  way  of  observa- 
tion or  experimentation.  The  following  quotation  gives  a 
fair  notion  of  the  extent  of  Mill's  retraction: 

The  conceptions  then  which  we  employ  for  the  colligation  and 
methodization  of  facts,  do  not  develop  themselves  from  within,  but 
are  impressed  upon  the  mind  from  without;  they  are  never  ob- 
tained otherwise  than  by  way  of  comparison  and  abstraction,  and, 
in  the  most  important  and  most  numerous  cases,  are  evolved  by  ab- 
straction from  the  very  phenomena  which  it  is  their  office  to  colli- 
gate.1 

Even  here  Mill's  sense  for  the  positive  side  of  scientific  in- 
quiry suffices  to  reveal  to  him  that  the  "facts"  are  some- 
how inadequate  and  defective,  and  are  in  need  of  assistance 
from  ideas  —  and  yet  the  ideas  which  are  to  help  out  the 
facts  are  to  be  the  impress  of  the  unsure  facts!  The  con- 
tradiction comes  out  very  clearly  when  Mill  says:  "The 
really  difficult  cases  are  those  in  which  the  conception  des- 
tined to  create  light  and  order  out  of  darkness  and  confu- 

i  Logic,  Book  IV,  chap.  2,  sec.  2 ;  italics  mine. 


THE  NATURE  OF  HYPOTHESIS 


sion  has  to  be  sought  for  among  the  very  phenomena  which 
it  afterward  serves  to  arrange."1 

Of  course,  there  is  a  sense  in  which  Mill's  view  is  very 
much  nearer  the  truth  than  is  Whewell's.  Mill  at  least  sees 
that  "  idea  "  must  be  relevant  to  the  facts  or  data  which  it  is 
to  arrange,  which  are  to  have  "light  and  order"  introduced 
into  them  by  means  of  the  idea.  He  sees  clearly  enough 
that  this  is  impossible  save  as  the  idea  develops  within  the 
same  experience  in  which  the  "dark  and  confused"  facts  are 
presented.  He  goes  on  to  show  correctly  enough  how  con- 
flicting data  lead  the  mind  to  a  "confused  feeling  of  an 
analogy  "  between  the  data  of  the  confused  experience  and 
of  some  other  experience  which  is  orderly  (or  already  colli- 
gated and  methodized)  ;  and  how  this  vague  feeling,  through 
processes  of  further  exploration  and  comparison  of  experi- 
ences, gets  a  clearer  and  more  adequate  form  until  we  finally 
accept  it.  He  shows  how  in  this  process  we  continually 
judge  of  the  worth  of  the  idea  which  is  in  process  of  forma- 
tion, by  reference  to  its  appropriateness  to  our  purpose.  He 
goes  so  far  as  to  say  :  "  The  question  of  appropriateness  is 
relative  to  the  particular  object  we  have  in  view."2  He  sums 
up  his  discussion  by  stating:  "We  cannot  frame  good  gen- 
eral conceptions  beforehand.  That  the  conception  we  have 
obtained  is  the  one  we  want  can  only  be  known  when  we  have 
done  the  work  for  the  sake  of  which  we  wanted  it"  : 

This  all  describes  the  actual  state  of  the  case,  but  it  is 
consistent  only  with  a  logical  theory  which  makes  the  dis- 
tinction between  fact  and  hypothesis  instrumental  in  the 
transformation  of  experience  from  a  confused  into  an  organ  - 
ized  form  ;  not  with  Mill's  notion  that  sensations  are  some- 
how finally  and  completely  given  as  ultimate  facts,  and 

1  Ibid. 

2  Ibid.,  sec.  4;    in  sec.  6  he  states  even  more  expressly  that  any  conception  is  ap- 
propriate in  the  degree  in  which  it  "  helps  us  toward  what  we  wish  to  understand." 

3  Ibid.,  sec.  6;  italics  mine. 


168  STUDIES  IN  LOGICAL  THEOKY 

that  ideas  are  mere  re-registrations  of  such  facts.  It  is 
perfectly  just  to  say  that  the  hypothesis  is  impressed  upon 
the  mind  (in  the  sense  that  any  notion  which  occurs  to  the 
mind  is  impressed)  in  the  course  of  an  experience.  It  is 
well  enough,  if  one  define  what  he  means,  to  say  that  the 
hypothesis  is  impressed  (that  is  to  say,  occurs  or  is  sug- 
gested) through  the  medium  of  given  facts,  or  even  of  sen- 
sations. But  it  is  equally  true  that  the  facts  are  presented 
and  that  sensations  occur  within  the  course  of  an  experience 
which  is  larger  than  the  bare  facts,  because  involving  the 
conflicts  among  them  and  the  corresponding  intention  to 
treat  them  in  some  fashion  which  will  secure  a  unified  expe- 
rience. Facts  get  power  to  suggest  ideas  to  the  mind  —  to 
"  impress"-  -  only  through  their  position  in  an  entire  expe- 
rience which  is  in  process  of  disintegration  and  of  recon- 
struction—  their  "fringe"  or  feeling  of  tendency  is  quite 
as  factual  as  they  are.  The  fact  that  "the  conception  we 
have  obtained  is  the  one  we  want  can  be  known  only  when 
we  have  done  the  work  for  the  sake  of  which  we  wanted  it," 
is  enough  to  show  that  it  is  not  bare  facts,  but  facts  in  rela- 
tion to  want  and  purpose  and  purpose  in  relation  to  facts, 
which  originate  the  hypothesis. 

It  would  be  interesting  to  follow  the  history  of  discus- 
sion of  the  hypothesis  since  the  time  of  Whewell  and  of  Mill, 
particularly  in  the  writings  of  Jevons,  Venn,  and  Bosanquet. 
This  history  would  refine  the  terms  of  our  discussion  by 
introducing  more  complex  distinctions  and  relations.  But 
it  would  be  found,  I  think,  only  to  refine,  not  to  introduce 
any  fundamentally  new  principles.  In  each  case,  we  find  the 
writer  struggling  with  the  necessity  of  distinguishing 
between  fact  and  idea;  of  giving  the  fact  a  certain  primacy 
with  respect  to  testing  of  idea  and  of  giving  the  idea  a  primacy 
with  respect  to  the  significance  and  orderliness  of  the  fact; 
and  of  holding  throughout  to  a  relationship  of  idea  with 


THE  NATUBE  OF  HYPOTHESIS  169 

fact  so  intimate  that  the  idea  develops  only  by  being  "com- 
pared "  with  facts  (that  is,  used  in  construing  them),  and  facts 
get  to  be  known  only  as  they  are  "  connected  "  through  the 
idea — and  we  find  that  what  is  a  maze  of  paradoxes  and 
inconsistencies  from  an  absolute,  from  a  non-historic  stand- 
point, is  a  matter  of  course  the  moment  it  is  looked  at  from 
the  standpoint  of  experience  engaged  in  self -transformation 
of  meaning  through  conflict  and  reconstitution. 

But  we  can  only  note  one  or  two  points.  Jevons's  "infi- 
nite ballot-box  "  of  nature  which  is  absolutely  neutral  as  to 
any  particular  conception  or  idea,  and  which  accordingly 
requires  as  its  correlate  the  formation  of  every  possible  hy- 
pothesis (all  standing  in  themselves  upon  the  same  level  of 
probability)  is  an  interesting  example  of  the  logical  conse- 
quences of  feeling  the  need  of  both  fact  and  hypothesis  for 
scientific  procedure  and  yet  regarding  them  as  somehow 
arising  independently  of  each  other.  It  is  an  attempt  to 
combine  extreme  empiricism  and  extreme  rationalism.  The 
process  of  forming  hypotheses  and  of  deducing  their  rational 
consequences  goes  on  at  random,  because  the  disconnectedness 
of  facts  as  given  is  so  ultimate  that  the  facts  suggest  one  hypo- 
thesis no  more  readily  than  another.  Mathematics,  in  its  two 
forms  of  measurements  as  applied  to  the  facts,  and  of  calcula- 
tion as  applied  in  deduction,  furnishes  Jevons  the  bridge  by 
which  he  finally  covers  the  gulf  which  he  has  first  himself  cre- 
ated. Venn's  theory  requires  little  or  no  restatement  to  bring 
it  into  line  with  the  position  taken  in  the  text.  He  holds  to 
the  origin  of  hypothesis  in  the  original  practical  needs  of 
mankind,  and  to  its  gradual  development  into  present  scien- 
tific form.1  He  states  expressly: 

The  distinction  between  what  is  known  and  what  is  not 
known  is  essential  to  Logic,  and  peculiarly  characteristic  of  it 

in  a  degree  not  to  be  found  in  any  other  science.     Inference  is  the 

• 

i  VENN,  Empirical  Logic,  p.  383. 


170  STUDIES  IN  LOGICAL  THEORY 

process  of  passing  from  one  to  the  other;  from  facts  which  we  had 
accepted  as  premises,  to  those  which  we  have  not  yet  accepted, 
but  are  in  the  act  of  doing  so  by  the  very  process  in  question.  No 
scrutiny  of  the  facts  themselves,  regarded  as  objective,  can  ever 
detect  these  characteristics  of  their  greater  or  less  familiarity  to 
our  minds.  We  must  introduce  also  the  subjective  element  if  we 
wish  to  give  any  adequate  explanation  of  them.1 

Venn,  however,  does  not  attempt  a  thoroughgoing  state- 
ment of  logical  distinctions,  relations,  and  operations,  as 
parts  "of  the  act  of  passing  from  the  unknown  to  the  known." 
He  recognizes  the  relation  of  reflection  to  a  historic  process, 
which  we  have  here  termed  "reconstruction,"  and  the  origin 
and  worth  of  hypothesis  as  a  tool  in  the  movement,  but  does 
not  carry  his  analysis  to  a  systematic  form. 

Ill 

Origin  of  the  hypothesis. —  In  our  analysis  of  the  process 
of  judgment,  we  attempted  to  show  that  the  predicate  arises 
in  case  of  failure  of  some  line  of  activity  going  on  in  terms 
of  an  established  habit.  When  the  old  habit  is  checked 
through  failure  to  deal  with  new  conditions  (i.  e.,  when  the 
situation  is  such  as  to  stimulate  two  habits  with  distinct 
aims)  the  problem  is  to  find  a  new  method  of  response  — 
that  is,  to  co-ordinate  the  conflicting  tendencies  by  building 
up  a  single  aim  which  will  function  the  existing  situation. 
As  we  saw  that,  in  case  of  judgment,  habit  when  checked 
became  ideal,  an  idea,  so  the  new  habit  is  first  formalized  as 
an  ideal  type  of  reaction  and  is  the  hypothesis  by  which  we 
attempt  to  construe  new  data.  In  our  inquiry  as  to  how  this 
formulation  is  effected,  i.  e. ,  how  the  hypothesis  is  developed, 
it  will  be  convenient  to  take  some  of  the  currently  accepted 
statements  as  to  their  origin,  and  show  how  these  statements 

stand  in  reference  to  the  analysis  proposed. 

• 

1  VENN,  Empirical  Logic,  p.  25 ;  italics  mine. 


THE  NATURE  OF  HYPOTHESIS       171 

Enumerative  induction  and  allied  processes. — It  is 
pointed  out  by  Wei  ton1  that  the  various  ways  in  which 
hypotheses  are  suggested  may  be  reduced  to  three  classes, 
viz.,  enumerative  induction,  conversion  of  propositions,  and 
analogy.  Under  the  head  of  " enumeration"  he  reminds  us 
that  "  every  observed  regularity  of  connection  between  phe- 
nomena suggests  a  question  as  to  whether  it  is  universal." 
There  are  numerous  instances  of  this  in  mathematics.  For 
example,  it  is  noticed  that  1  +  3  =  22,  1  +  3  +  5  =  32,  1  +  3  + 
5  +  7=42,  etc.;  and  one  is  led  to  ask  whether  there  is  any 
general  principle  involved,  so  that  the  sum  of  the  first  n  odd 
numbers  will  be  n2,  where  n  is  any  number,  however  great. 
In  this  early  form  of  inductive  inference  there  are  two  diver- 
gent tendencies.  One  is  the  tendency  to  complete  enumera- 
tion. This  tendency  is  clearly  ideal — it  transcends  the  facts 
as  given.  To  look  for  all  the  cases  is  thus  itself  an  experi- 
mental inquiry,  based  upon  a  hypothesis  which  it  endeavors 
to  test.  But  in  most  cases  enumeration  can  be  only  incom- 
plete, and  we  are  able  to  reach  nothing  better  than  proba- 
bility. Hence  the  other  tendency  in  the  direction  of  an 
analysis  of  content  in  search  for  a  principle  of  connection  in 
the  elements  in  any  one  case.  For  if  a  characteristic  belong- 
ing to  a  number  of  individuals  suggests  a  class  where  it 
belongs  to  all  individuals,  it  must  be  that  it  is  found  in 
every  individual  as  such.  The  hypothesis  of  complete  class 
involves  a  hypothesis  as  to  the  character  of  each  individual 
in  the  class.  Thus  a  hypothesis  as  to  extension  transforms 
itself  into  one  as  to  intension. 

But  it  is  analogy  which  Welton  considers  "the  chief 
source  from  which  new  hypotheses  are  drawn."  In  the 
second  tendency  mentioned  under  enumerative  induction, 
that  is,  the  tendency  to  analysis  of  content  or  intension,  we 
are  naturally  led  to  analogy,  for  in  our  search  for  the  char- 

i  WELTOX,  Manual  of  Logic,  Vol.  II,  chap.  3.  y 

THC 

UNIVERSITY 
or 


172  STUDIES  IN  LOGICAL  THEORY 

acteristic  feature  which  determines  classification  among  the 
concrete  particulars  our  first  step  will  be  an  inference  by 
analogy.  In  analogy  attention  is  turned  from  the  number 
of  observed  instances  to  their  character,  and,  because  par- 
ticulars have  some  feature  in  common,  they  are  supposed  to 
be  the  same  in  still  other  respects.  While  the  best  we  can 
reach  in  analogy  is  probability,  the  arguments  may  be  such 
as  to  result  in  a  high  degree  of  certainty.  The  form  of  the 
argument  is  valuable  in  so  far  as  we  are  able  to  distinguish 
between  essential  and  nonessential  characteristics  on  which 
to  base  our  analogy.  What  is  essential  and  what  nonessen- 
tial depends  upon  the  particular  end  we  have  in  view. 

In  addition  to  enumerative  induction,  which  Welton  has 
mentioned,  it  is  to  be  noted  that  there  are  a  number  of  other 
processes  which  are  very  similar  to  it  in  that  a  number  of 
particulars  appear  to  furnish  a  basis  for  a  general  principle 
or  method.  Such  instances  are  common  in  induction,  in 
instruction,  and  in  methods  of  proof. 

If  one  is  to  be  instructed  in  some  new  kind  of  labor,  he 
is  supposed  to  acquire  a  grasp  of  the  method  after  having 
been  shown  in  a  few  instances  how  this  particular  work  is  to 
be  done;  and,  if  he  performs  the  manipulations  himself,  so 
much  the  better.  It  is  not  asked  why  the  experience  of  a 
few  cases  should  be  of  any  assistance,  for  it  seems  self- 
evident  that  an  experienced  man,  a  man  who  has  acquired 
the  skill,  or  knack,  of  doing  things,  should  deal  better  with 
all  other  cases  of  similar  nature. 

There  is  something  very  similar  in  inductive  proofs,  as 
they  are  called.  The  inductive  proof  is  common  in  algebra. 
Suppose  we  are  concerned  in  proving  the  law  of  expansion 
of  the  binomial  theorem.  We  show  by  actual  calculation 
that,  if  the  law  holds  good  for  the  nih  power,  it  is  true  for 
the  n  -f-  first  power.  That  is,  if  it  holds  for  any  power,  it 
holds  for  the  next  also.  But  we  can  easily  show  that  it  does 


THE  NATURE  OF  HYPOTHESIS  173 

hold  for,  say,  the  second  power.  Then  it  must  be  true  for 
the  third,  and  hence  for  the  fourth,  and  so  on.  Whether 
this  law,  though  discovered  by  inductive  processes,  depends 
on  deduction  for  the  conclusiveness  of  its  proof,  as  Jevons 
holds;1  whether,  as  Erdmann2  contends,  the  proof  is  thor- 
oughly deductive;  or  whether  Wundt3  is  right  in  maintain- 
ing that  it  is  based  on  an  exact  analogy,  while  the 
fundamental  axioms  of  mathematics  are  inductive,  it  is  clear 
that  in  such  proofs  a  few  instances  are  employed  to  give  the 
learner  a  start  in  the  right  direction.  Something  suggests 
itself,  and  is  found  true  in  this  case,  in  the  next,  and  again 
in  the  next,  and  so  on.  It  may  be  questioned  whether  there 
is  usually  a  very  clear  notion  of  what  is  involved  in  the  "so 
on."  To  many  it  appears  to  mark  the  point  where,  after 
having  been  taken  a  few  steps,  the  learner  is  carried  on  by 
the  acquired  momentum  somewhat  after  the  fashion  of  one 
of  Newton's  laws  of  motion.  Whether  the  few  successive 
steps  are  an  integral  part  of  the  proof  or  merely  serve  as 
illustration,  they  are  very  generally  resorted  to.  In  fact, 
they  are  often  employed  where  there  is  no  attempt  to  intro- 
duce a  general  term  such  as  n,  or  fc,  or  Z,  but  the  few  indi- 
vidual instances  are  deemed  quite  sufficient.  Such,  for 
instance,  is  the  custom  in  arithmetical  processes.  We  call 
attention  to  these  facts  in  order  to  show  that  successive 
cases  are  utilized  in  the  course  of  explanation  as  an  aid  in 
establishing  the  generality  of  a  law. 

In  geometry  we  find  a  class  of  proofs  in  which  the  suc- 
cessive steps  seem  to  have  great  significance.  A  common 
proof  of  the  area  of  the  circle  will  serve  as  a  fair  example. 
A  regular  polygon  is  circumscribed  about  the  circle.  Then 
as  the  number  of  its  sides  are  increased  its  area  will  approach 

i  W.  S.  JEVOXS,  Principles  of  Science,  pp.  231,  232. 

2B.  ERDMAXX,  "Zur  Theorie  des  Syllogismus  und  der  Induktion,"  Philoso- 
phische  Abhandlungen,  Vol.  VI,  p.  230. 

3  WCXDT,  Logik,  2d  ed.,  Vol.  II,  p.  131. 


174  STUDIES  IN  LOGICAL  THEORY 

that  of  the  circle,  as  its  perimeter  approaches  the  circumfer- 
ence of  the  circle.  t  The  area  of  the  circle  is  thus  inferred  to 
be  7T.R2,  since  the  area  of  the  polygon  is  always  ij-Rx  perim- 
eter, and  in  case  of  the  circle  the  circumference  =27rP. 
Here  again  we  get  under  such  headway  by  means  of  the 
polygon  that  we  arrive  at  the  circle  with  but  little  difficulty. 
Had  we  attempted  the  transition  at  once,  say,  from  a  cir- 
cumscribed square,  we  should  doubtless  have  experienced 
some  uncertainty  and  might  have  recoiled  from  what  would 
seem  a  rash  attempt;  but  as  the  number  of  the  sides  of  our 
polygon  approach  infinity — that  mysterious  realm  where 
many  paradoxical  things  become  possible — the  transition 
becomes  so  easy  that  our  polygon  is  often  said  to  have  truly 
become  a  circle. 

Similarly,  some  statements  of  the  infinitesimal  calculus 
rest  on  the  assumption  that  slight  degrees  of  difference  may 
be  neglected.  Though  the  more  modern  theory  of  limits 
has  largely  displaced  this  attitude  in  calculus  and  has  also 
changed  the  method  of  proof  in  such  geometrical  problems 
as  the  area  of  the  circle,  the  underlying  motive  seems  to 
have  been  to  make  transitions  easy,  and  thus  to  make  possible 
a  continued  application  of  some  particular  method  or  way  of 
dealing  with  things. 

But  granted  that  this  is  all  true,  what  has  it  to  do  with 
the  origin  of  the  hypothesis?  It  seems  likely  that  the 
hypothesis  may  be  suggested  by  a  few  successive  instances; 
but  are  these  to  be  classed  with  the  successive  steps  in  proof 
to  which  we  have  referred?  In  the  first  place,  we  attempt 
to  prove  our  hypothesis  because  we  are  not  sure  it  is  true ; 
we  are  not  satisfied  that  there  are  no  other  tenable  hypothe- 
ses. But  if  we  do  test  it,  is  not  such  test  enough?  It 
depends  upon  how  thorough  a  grasp  we  have  of  the  situa- 
tion; but,  in  general,  each  test  case  adds  to  its  probability. 
The  value  of  tests  lies  in  the  fact  that  they  strengthen  and 


UNIVERSITY 

Of 


THE  NATURE  OF  HYPOTHESIS  175 

tend  to  confirm  our  hypothesis  by  checking  the  force  of 
alternatives.  One  instance  is  not  sufficient  because  there 
are  other  possible  incipient  hypotheses,  or  more  properly 
tendencies,  and  the  enumeration  serves  to  bring  one  of  these 
tendencies  into  prominence  in  that  it  diminishes  other  vague 
and  perhaps  subconscious  tendencies  and  strengthens  the 
one  which  suddenly  appears  as  the  mysterious  product  of 
genius. 

The  question  might  arise  why  the  mere  repetition  of  con- 
flicting tendencies  would  lead  to  a  predominance  of  one  of 
them.  Why  would  they  not  all  remain  in  conflict  and  con- 
tinue to  check  any  positive  result?  It  is  probably  because 
there  never  is  any  absolute  equilibrium.  The  successive 
instances  tend  to  intensify  and  bring  into  prominence  some 
tendency  which  is  already  taking  a  lead,  so  to  speak.  And 
it  may  be  said  further  in  this  connection  that  only  as  seen 
from  the  outside,  only  as  a  mechanical  view  is  taken,  does 
there  appear  to  be  an  excluding  of  definitely  made  out  alter- 
natives. 

In  explanation  of  the  part  played  by  analogy  in  the  origin 
of  hypotheses,  Welton  points  out  that  a  mere  number  of 
instances  do  not  take  us  very  far,  and  that  there  must  be 
some  "specification  of  the  instances  as  well  as  numbering  of 
them,"  and  goes  on  to  show  that  the  argument  by  enumera- 
tive  induction  passes  readily  into  one  from  analogy,  as  soon 
as  attention  is  turned  from  the  number  of  the  observed 
instances  to  their  character.  It  is  not  necessary,  however, 
to  pass  to  analogy  through  enumerative  induction.  "  When 
the  instances  presented  to  observation  offer  immediately  the 
characteristic  marks  on  which  we  base  the  inference  to  the 
connection  of  S  and  P,  we  can  proceed  at  once  to  an  infer- 
ence from  analogy,  without  any  preliminary  enumeration  of 
the  instances." 1 

i  WELTON,  Manual  of  Logic,  Vol.  II,  p.  72. 


176  STUDIES  IN  LOGICAL  THEORY 

Welton,  and  logicians  generally,  regard  analogy  as  an 
inference  on  the  basis  of  partial  identity.  Because  of  cer- 
tain common  features  we  are  led  to  infer  a  still  greater  like- 
ness. 

Both  enumerative  induction  and  analogy  are  explicable 
in  terms  of  habit.  We  saw  in  our  examination  of  enume- 
rative induction  that  a  form  of  reaction  gains  strength 
through  a  series  of  successful  applications.  Analogy  marks 
the  presence  of  an  identical  element  together  with  the  ten- 
dency to  extend  this  "partial  identity"  (as  it  is  commonly 
called)  still  farther.  In  other  words,  in  analogy  it  is  sug- 
gested that  a  type  of  reaction  which  is  the  same  in  certain 
respects  may  be  made  similar  in  a  greater  degree.  In  enu- 
merative induction  we  lay  stress  on  the  number  of  instances 
in  which  the  habit  is  applied.  In  analogy  we  emphasize  the 
content  side  and  take  note  of  the  partial  identity.  In  fact, 
the  relation  between  enumerative  induction  and  analogy  is 
of  the  same  sort  as  that  existing  between  association  by  con- 
tiguity and  association  by  similarity.  In  association  by 
contiguity  we  think  of  the  things  associated  as  merely  stand- 
ing in  certain  temporal  or  spatial  relations,  and  disregard  the 
fact  that  they  were  elements  in  a  larger  experience.  In  case 
of  association  by  similarity  we  regard  the  like  feature  in  the 
things  associated  as  a  basis  for  further  correction. 

In  conversion  of  propositions  we  try  to  reverse  the  direc- 
tion of  the  reaction,  so  to  speak,  and  thereby  to  free  the  habit, 
to  get  a  mode  of  response  so  generalized  as  to  act  with  a 
minimum  cue.  For  instance,  we  can  deal  with  A  in  a 
way  called  B,  or,  in  other  words,  in  the  same  way  that 
we  did  with  other  things  called  B.  If  we  say,  "Man  is 
an  animal,"  then  to  a  certain  extent  the  term  "animal" 
signifies  the  way  in  which  we  regard  "man."  But  the 
question  arises  whether  we  can  regard  all  animals  as  we 
do  man.  Evidently  not,  for  the  reaction  which  is  fitting  in 


THE  NATUKE  OF  HYPOTHESIS  177 

case  of  animals  would  be  only  partially  applicable  to  man. 
With  the  animals  that  are  also  men  we  have  the  beginning 
of  a  habit  which,  if  unchecked,  would  lead  to  a  similar  reac- 
tion toward  all  animals,  i.  6.,  we  would  say:  "All  animals 
are  men."  Man  may  be  said  to  be  the  richer  concept,  in 
that  only  a  part  of  the  reaction  which  determines  an  object 
to  be  a  man  is  required  to  designate  it  as  an  animal.  On 
the  other  hand,  if  we  start  with  animal,  then  (except  in  case 
of  the  animals  which  are  men)  there  is  lacking  the  subject- 
matter  which  would  permit  the  fuller  concept  to  be  applied. 
By  supplying  the  conditions  under  which  animal  =  man  we 
get  a  reversible  habit.  The  equation  of  technical  science  has 
just  this  character.  It  represents  the  maximum  freeing  or 
abstraction  of  a  predicate  qua  predicate,  and  thereby  multi- 
plies the  possible  applications  of  it  to  subjects  of  future 
judgments,  and  lessens  the  amount  of  shearing  away  of 
irrelevancies  and  of  re-adaptation  necessary  when  so  used 
in  any  particular  case. 

Formation  and  test  of  the  hypothesis. — The  formation  of 
the  hypothesis  is  commonly  regarded  as  essentially  different 
from  the  process  of  testing,  which  it  subsequently  under- 
goes. We  are  said  to  observe  facts,  invent  hypotheses,  and 
then  test  them.  The  hypothesis  is  not  required  for  our  pre- 
liminary observations;  and  some  writers,  regarding  the 
hypothesis  as  a  formulation  which  requires  a  difficult  and 
elaborate  test,  decline  to  admit  as  hypotheses  those  more 
simple  suppositions,  which  are  readily  confirmed  or  rejected. 
A  very  good  illustration  of  this  point  of  view  is  met  with  in 
Wundt's  discussion  of  the  hypothesis,  by  an  examination  of 
which  we  hope  to  show  that  such  distinctions  are  rather  arti- 
ficial than  real. 

The  subject-matter  of  science,  says  Wundt,1  is  constituted 
by  that  which  is  actually  given  and  that  which  is  actually  to 

i  Op.  cit.,  Vol.  I,  p.  452  ff. 

— 1TffTw  Y- 
or  — 


UNIVERSITY 


178  STUDIES  IN  LOGICAL  THEORY 

be  expected.  The  whole  content  is  not  limited  to  this, 
however,  for  these  facts  must  be  supplemented  by  certain 
presuppositions,  which  are  not  given  in  a  factual  sense. 
Such  presuppositions  are  called  hypotheses  and  are  justified 
by  our  fundamental  demand  for  unity.  However  valuable 
the  hypothesis  may  be  when  rightly  used,  there  is  constant 
danger  of  illegitimately  extending  it  by  additions  that  spring 
from  mere  inclinations  of  fancy.  Furthermore,  the  hypothe- 
sis in  this  proper  scientific  sense  must  be  carefully  dis- 
tinguished from  the  various  inaccurate  uses,  which  are 
prevalent.  For  instance,  hypotheses  must  not  be  confused 
with  expectations  of  fact.  As  cases  in  point  Wundt  men- 
tions Galileo's  suppositions  that  small  vibrations  of  the 
pendulum  are  isochronous,  and  that  the  space  traversed  by 
a  falling  body  is  proportional  to  the  square  of  the  time  it 
has  been  falling.  It  is  true  that  such  anticipations  play  an 
important  part  in  science,  but  so  long  as  they  relate  to  the 
facts  themselves  or  to  their  connections,  and  can  be  con- 
firmed or  rejected  any  moment  through  observation,  they 
should  not  be  classed  with  those  added  presuppositions 
which  are  used  to  co-ordinate  facts.  Hence  not  all  supposi- 
tions are  hypotheses.  On  the  other  hand,  not  every 
hypothesis  can  be  actually  experienced.  For  example,  one 
employs  in  physics  the  hypothesis  of  electric  fluid,  but  does 
not  expect  actually  to  meet  with  it.  In  many  cases,  how- 
ever, the  hypothesis  becomes  proved  as  an  experienced  fact. 
Such  was  the  course  of  the  Copernican  theory,  which  was  at 
first  only  a  hypothesis,  but  was  transformed  into  fact 
through  the  evidence  afforded  by  subsequent  astronomical 
observation. 

Wundt  defines  a  theory  as  a  hypothesis  taken  together 
with  the  facts  for  whose  elucidation  it  was  invented.  In 
thus  establishing  a  connection  between  the  facts  which  the 
hypothesis  merely  suggested,  the  theory  furnishes  at  the 


THE  NATURE  OF  HYPOTHESIS  179 

same  time  partly  the  foundation  (Begrundung)  and  partly 
the  confirmation  (Bestdtigung)  of  the  hypothesis.1  These 
aspects,  Wundt  insists,  must  be  sharply  distinguished. 
Every  hypothesis  must  have  its  Begrundung,  but  there  can 
be  Bestdtigung  only  in  so  far  as  the  hypothesis  contains 
elements  which  are  accessible  to  actual  processes  of  verifica- 
tion. In  most  cases  verification  is  attainable  in  only  cer- 
tain elements  of  the  hypothesis.  For  example,  Newton  was 
obliged  to  limit  himself  to  one  instance  in  the  verification  of 
his  theory  of  gravitation,  viz.,  the  movements  of  the  moon. 
The  other  heavenly  bodies  afforded  nothing  better  than  a 
foundation  in  that  the  supposition  that  gravity  decreases  as 
the  square  of  the  distance  increases  enabled  him  to  deduce 
the  movements  of  the  planets.  The  main  object  of  his 
theory,  however,  lay  in  the  deduction  of  these  movements 
and  not  in  the  proof  of  universal  gravity.  With  the  Dar- 
winian theory,  on  the  contrary,  the  main  interest  is  in  seek- 
ing its  verification  through  examination  of  actual  cases  of 
development.  Thus,  while  the  Newtonian  and  the  greater 
part  of  the  other  physical  theories  lead  to  a  deduction  of 
the  facts  from  the  hypotheses,  which  can  be  verified  only 
in  individual  instances,  the  Darwinian  theory  is  concerned 
in  evolving  as  far  as  possible  the  hypothesis  out  of  the 
facts. 

Let  us  look  more  closely  at  Wundt's  position.  We  will 
ask,  first,  whether  the  distinction  between  hypotheses  and 
expectations  is  as  pronounced  as  he  maintains ;  and,  second, 
whether  the  relation  between  Begrundung  and  Bestdtigung 
may  not  be  closer  than  Wundt  would  have  us  believe. 

As  examples  of  the  hypothesis  Wundt  mentions  the 
Copernican  hypothesis,  Newton's  hypothesis  of  gravitation, 
and  the  predictions  of  the  astronomers  which  led  to  the  dis- 
covery of  Neptune.  As  examples  of  mere  expectations  we 

i  Op.  cit.,  Vol.  I,  pp.  454-461. 


180  STUDIES  IN  LOGICAL  THEORY 

are  referred  to  Galileo's  experiments  with  falling  bodies  and 
pendulums.  In  case  of  Newton's  hypothesis  there  was  the 
assumption  of  a  general  law,  which  was  verified  after  much 
labor  and  delay.  The  heliocentric  hypothesis  of  Coperni- 
cus, which  was  invented  for  the  purpose  of  bringing  system 
and  unity  into  the  movements  of  the  planets,  has  also  been 
fairly  well  substantiated.  In  the  discovery  of  Neptune  we 
have,  apparently,  not  the  proof  of  a  general  law  or  the  dis- 
covery of  further  peculiarities  of  previously  known  data,  but 
rather  the  discovery  of  a  new  object  or  agent  by  means  of 
its  observed  effects.  In  each  of  these  instances  we  admit 
that  the  hypothesis  was  not  readily  suggested  or  easily 
and  directly  tested. 

If  we  turn  to  Galileo's  pendulum  and  falling  bodies,  it  is 
clear  first  of  all  that  he  did  not  have  in  mind  the  discovery 
of  some  object,  as  was  the  case  in  the  discovery  of  Neptune. 
Did  he,  then,  either  contribute  to  the  proof  of  a  general  law 
or  discover  further  characteristics  of  things  already  known 
in  a  more  general  way?  Wundt  tells  us  that  Galileo  only 
determined  a  little  more  exactly  what  he  already  knew,  and 
that  he  did  this  with  but  little  labor  or  delay. 

What,  then,  is  the  real  difference  between  hypothesis  and 
expectation?  If  we  compare  Galileo's  determination  of  the 
law  of  falling  bodies  with  Newton's  test  of  his  hypothesis  of 
gravitation,  we  see  that  both  expectation  and  hypothesis 
were  founded  on  observation  and  took  the  form  of  mathe- 
matical formulae.  Each  tended  to  confirm  the  general  law 
expressed  in  its  formula,  though  there  was,  of  course,  much 
difference  in  the  time  and  labor  required.  If  we  compare 
the  Copernican  hypothesis  with  Galileo's  supposition  con- 
cerning the  pendulum,  we  find  again  that  they  agree  in 
regard  to  general  purpose  and  method,  and  differ  in  the 
difficulty  of  verification.  If  the  experiment  with  the  pen- 
dulum only  substituted  exactness  for  inexactness,  did  the 


THE  NATUKE  OF  HYPOTHESIS  181 

Copernican  theory  do  anything  different  in  kind  ?  It  is  true 
that  the  more  exact  statement  of  the  swing  of  the  pendulum 
was  expressed  in  quantitative  form,  but  quantitative  state- 
ment is  no  criterion  of  either  the  presence  or  the  absence  of 
the  hypothesis. 

Again,  we  may  compare  the  pendulum  with  Kepler's  laws. 
What  was  Kepler's  hypothesis,  that  the  square  of  the  periodic 
times  of  the  several  planets  are  proportional  to  the  cubes  of 
their  mean  distances  from  the  sun,  except  a  more  exact  for- 
mulation of  facts  which  were  already  known  in  a  more  gen- 
eral way?  Wundt's  position  seems  to  be  this:  whenever  a 
supposition  or  suggestion  can  be  tested  readily,  it  should 
not  be  classed  as  a  hypothesis.  This  would  make  the  dis- 
tinction one  of  degree  rather  than  kind,  and  it  does  not 
appear  how  much  labor  we  must  expend,  or  how  long  our 
supposition  must  evade  our  efforts  to  test  it,  before  it  can 
win  the  title  of  hypothesis. 

In  the  second  place,  we  have  seen  that  Wundt  draws  a 
sharp  line  between  Begrilndung  and  Best&tigung :  It  is 
doubtless  true  that  every  hypothesis  requires  a  certain  justi- 
fication, for  unless  other  facts  can  be  found  which  agree 
with  deductions  made  in  accordance  with  it,  its  only  sup- 
port would  be  the  data  from  which  it  is  drawn.  Such  sup- 
port as  this  would  be  obtained  through  a  process  too  clearly 
circular  to  be  seriously  entertained.  The  distinction  which 
Wundt  draws  between  Begrilndung  and  Bestatigung  is 
evidently  due  to  the  presence  of  the  experimental  element 
in  the  latter.  For  descriptive  purposes  this  distinction  is 
useful,  but  is  misleading  if  it  is  understood  to  mean  that 
there  is  mere  experience  in  one  case  and  mere  inference  in  the 
other.  The  difference  is  rather  due  to  the  relative  parts  played 
by  inference  and  by  accepted  experience  in  each.  In  Begriin- 
dung  the  inferential  feature  is  the  more  prominent,  while  in 
Bestatigung  the  main  emphasis  is  on  the  experiential  aspect. 


182  STUDIES  IN  LOGICAL  THEORY 

It  must  not  be  supposed,  however,  that  either  of  these 
aspects  can  be  wholly  absent.  It  is  difficult  to  understand 
how  any  hypothesis  can  be  entertained  at  all  unless  it  meets 
in  some  measure  the  demand  with  reference  to  which  it  was 
invented,  viz.,  a  unification  of  conflicts  in  experience.  And, 
in  so  far,  it  is  confirmed.  The  motive  which  casts  doubt 
upon  its  adequacy  is  the  same  that  leads  to  its  re-forming 
as  a  hypothesis,  as  a  mental  concept. 

The  difficulties  in  Wundt's  position  are  thus  due  to  a 
failure  to  take  account  of  the  reconstructive  nature  of  the 
judgment.  The  predicate,  supposition,  or  hypothesis,  what- 
ever we  may  choose  to  call  it,  is  formed  because  of  the  check 
of  a  former  habit.  The  judgment  is  an  ideal  application  of 
a  new  habit,  and  its  test  is  the  attempt  to  act  in  accordance 
with  this  ideal  reconstruction.  It  must  not  be  thought,  how- 
ever, that  our  supposition  is  first  fully  developed  and  then 
tried  and  accepted  or  rejected  without  modification.  On 
the  contrary,  its  growth  is  the  result  of  successive  minor 
tests  and  corresponding  minor  modifications  in  its  form. 
Formation  and  test  are  merely  convenient  distinctions  in  a 
larger  process  in  which  forming,  testing,  and  re-forming  go 
on  together.  The  activity  of  experimental  verification  is  not 
only  a  testing,  a  confirming  or  weakening  of  the  validity  of 
a  hypothesis,  but  it  is  equally  well  an  evolution  of  the  mean- 
ing of  the  hypothesis  through  bringing  it  into  closer  rela- 
tions with  specific  data  not  previously  included  in  defining 
its  import.  Per  contra,  a  purely  reflective  and  deductive 
consideration  which  develops  the  idea  as  hypothesis,  in 
so  far  as  it  introduces  the  determinateness  of  previously 
accepted  facts  within  the  scope,  comprehension,  or  intension 
of  the  idea,  is  in  so  far  forth,  a  verification. 

If  the  view  which  we  have  maintained  is  correct,  the  hypo- 
thesis is  not  to  be  limited  to  those  elaborate  formulations  of 
the  scientist  which  he  seeks  to  confirm  by  crucial  tests.  The 


THE  NATURE  OF  HYPOTHESIS  183 

hypothesis  of  the  investigator  differs  from  the  comparatively 
rough  conjecture  of  the  plain  man  only  in  its  greater  preci- 
sion. Indeed,  as  we  have  attempted  to  show,  the  hypothesis 
is  not  a  method  which  we  may  employ  or  not  as  we  choose; 
on  the  contrary,  as  predicate  of  the  judgment  it  is  present 
in  a  more  or  less  explicit  form  if  we  judge  at  all.  Whether 
the  time  and  labor  required  for  its  confirmation  or  rejection 
is  a  matter  of  a  lifetime  or  a  moment,  its  nature  remains  the 
same.  Its  function  is  identical  with  that  of  the  predicate. 
In  short,  the  hypothesis  is  the  predicate  so  brought  to  con- 
sciousness and  defined  that  those  features  which  are  not 
noticed  in  the  ordinary  judgment  are  brought  into  promi- 
nence. We  then  recognize  the  hypothesis  to  be  what  in 
fact  the  predicate  always  is,  viz.,  a  method  of  organization 
and  control. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


•  - 

1953 


REC'D  UD 

lift  25 1969 

REC'D  UD 


REC'D  LD 

2  3 '63  -4  PM 


LD  21-100m-7,'52(A2528sl6)476 


YC  30993 


m 


, 


m 


